Which sum does the model below represent?

4 positive tiles and 7 negative tiles.
4 + (negative 7) = negative 3
4 + 7 = 11
8 + (negative 3) = 4
11 + (negative 4) = negative 3

We are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).

To find the confidence interval, we can use the formula:

CI = p ± zsqrt(p(1-p)/n)

Where:

CI: Confidence Interval

p: Proportion of students who correctly identified the flavor (sample proportion)

z: Z-score corresponding to the desired confidence level (95% confidence level corresponds to z=1.96)

n: Sample size

Plugging in the values we have:

p = 78/154 = 0.5065

z = 1.96

n = 154

CI = 0.5065 ± 1.96sqrt(0.5065(1-0.5065)/154)

CI = 0.5065 ± 0.0783

CI = (0.4282, 0.5848)

Therefore, we are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).

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Answer:

Step-by-step explanation:

Answer:

Domain: 4

Range: 0

Step-by-step explanation:

The Domain is the first coordinate which is x

The Range is the second coordinate which is y

Hope This Helps :)

Answer:

65569898

Step-by-step explanation:

1753x87694=66033582

66033582-463684=65569898

Answer:

1. Correct

2. C.

3. C.

4. Correct

5. Incorrect. Answer: C. (The constant term is the term with no variable.)

6. C.

7. B.

8. A.

9. B.

10. B.

Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.

Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)

whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as

:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1

(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,

the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:

A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17

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The value of the simplified expression is -15.

The simplification of the expression is determined by substituting the appropriate values of the variables into the equation.

The given expression; = 54/g - 8h

The value of g = 6 and the value of h = 3,

The value of the expression is calculated as follows;

= 54/g - 8h

= 54/6 - 8(3)

= 9 - 24

= - 15

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The complete question is below:

54/g - 8h, when g = 6 and h=3

Hey there! I'm happy to help!

To solve by substitution, rearrange one of the equations for one of the variables.

3x+2y=11

Subtract 2y from both sides.

3x=11-2y

Divide both sides by 3.

x=11/3-2/3y

Now we plug this value of x into the second equation to solve for y.

2(11/3-2/3y)-2y=14

We use distributive property to undo the parentheses.

22/3-4/3y-2y=14

We combine like terms.

22/3-10/3y=14

We subtract 22/3 from both sides.

-10/3y=20/3

Divide both sides by -10/3.

y=-2

We plug this value into one of the equations to solve for x.

3x+2(-2)=11

3x-4=11

Add 4 to both sides.

3x=15

Divide both sides by 3.

x=5

So, the solution is x=5 and y=-2 or (5,-2).

Have a wonderful day! :D

Answer:

\({ \tt{ {x}^{2} + {y}^{2} = 25 - - - \{eqn(a) \}}} \\ { \tt{y = {x}^{2} + 3 - - - \{eqn(b) \} }}\)

» substitute y in eqn(a) with y in eqn(b)

\({ \tt{ {x}^{2} + ( {x}^{2} + 3) {}^{2} = 25}} \\ { \tt{ {x}^{2} + ( {x}^{2} + 6x + 9) = 25}} \\ { \tt{2 {x}^{2} + 6x + 9 = 25 }} \\ { \tt{2 {x}^{2} + 6x - 16 = 0}} \\ { \tt{x = 1.7 \: \: and \: \: - 4.7}}\)

» Find y in eqn(b)

\({ \tt{y = {x}^{2} + 3 }} \\ { \tt{y = 5.89 \: \: and \: \: 25.09}}\)

The height of the trapezoidal is 4.33 feet. Then the area of the tarp to cover the pool is 51.96 square feet.

It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a trapezoidal, one pair of opposite sides are parallel.

A hotel builds an isosceles trapezoidal pool for children. It orders a tarp to cover the pool when not in use.

Then the area of the trapezoidal will be

Area = 0.5(sum of parallel sides) height

Then the height of the trapezoidal will be

\(\rm h = 5 \times \sin 60 \\\\h = 4.33 \ ft\)

Then the area of the trapezoidal will be

Area = 0.5 × (10 + 12) × 4.33

Area = 51.96 ft²

The area of the tarp to cover the pool is 51.96 square feet.

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Answer:

1. 120 degrees

2. 4.3

3. 47.3

Step-by-step explanation:

PLATO/EDMENTUM

The LU factorization of matrix A is A = LU, where L = [[1, 0, 0], [-2, 1, 0], [1.5, -3, 1]] and U = [[4, -8, 10], [0, 24, -27], [0, 0, -12.5]].

Let's go step by step to find the LU factorization of matrix A.

Matrix A:

A =

[4, -8, 10]

[-8, 8, -7]

[6, -7, 3]

Step 1:

Initialize the L matrix as an identity matrix of the same size as A.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 2:

Perform Gaussian elimination to obtain U.

- Multiply the first row of A by (1/4) and replace the first row of A with the result.

A =

[1, -2, 2.5]

[-8, 8, -7]

[6, -7, 3]

- Subtract 8 times the first row of A from the second row of A and replace the second row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[6, -7, 3]

- Subtract 6 times the first row of A from the third row of A and replace the third row of A with the result.

A =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Step 3:

Update the L matrix based on the operations performed during Gaussian elimination.

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

Step 4:

The resulting matrix A is the upper triangular matrix U.

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

Therefore, the LU factorization of matrix A is:

L =

[1, 0, 0]

[0, 1, 0]

[0, 0, 1]

U =

[1, -2, 2.5]

[0, 24, -27]

[0, 5, -12.5]

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Answer:

\((f\circ g)(-5)=85\)

Step-by-step explanation:

We are given:

\(\displaystyle f(x)=4x+5\text{ and } g(x)=x^2+x\)

And we want to find:

\((f\circ g)(-5)\)

This is equivalent to:

\(\displaystyle =f(g(-5))\)

So, we will evaluate g(-5) first, which yields:

\(\displaystyle g(-5)=(-5)^2+(-5)=25-5=20\)

So:

\(=f(g(-5))=f(20)\)

Then:

\(\displaystyle f(20)=4(20)+5=80+5=85\)

Therefore:

\((f\circ g)(-5)=85\)

$1.76. A sales tax is a sum of money that a government organization takes in on the sale of particular goods. For instance, a state might impose a tax on all cars bought there. The tax rate is frequently expressed as a percentage of the price.

How to Determine Sales Tax:

Add the tax rate to the cost of your good or service. If the tax rate is expressed as a percentage, convert it to decimal form by multiplying the result by 100. 

1. Find the list price and the tax rate.

2. To obtain the tax rate as a decimal, divide the tax percentage by 100.

3. To calculate tax, multiply the list price by the decimal tax rate.

4. For the final price, multiply the list price by the tax rate.

=> Price before tax: $ 1.61

=> + Sales tax (9.5%): $ 0.15

=> Total price including tax: $ 1.76.

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Answer:x=-4

Step-by-step explanation:

Answer

196

Step-by-step explanation:

Answer:

28 g. ................

U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

A = {1, 3, 5, 7, 9}

B = {2, 4, 5, 6, 7}.

A = {1, 3, 5, 7, 9}

B' = {1,3,8,9,10}

A U B' = {1,3,5,7,8,9,10}

Answer:

A U B' = {1,3,5,7,8,9,10}

Answer:

1 1/2

Step-by-step explanation:

The linear inequality for the graph in this problem is given as follows:

y ≥ 2x/3 + 1.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

The graph crosses the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

When x increases by 3, y increases by 2, hence the slope m is given as follows:

m = 2/3.

Then the linear function is given as follows:

y = 2x/3 + 1.

Numbers above the solid line are graphed, hence the inequality is given as follows:

y ≥ 2x/3 + 1.

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Answer:

9.913 × 108

Step-by-step explanation:

Answer: 13/15

Step-by-step explanation:

26/30

Simple by 2

13/15

Answer:

26/30 = 13/15

Comparing the total earning of bith Steve and Carly using the equality sign, Steve's earning would be more than Carl's after 25 hours.

Steve :

Carly :

Let the number of hours worked = w

16w + 150 = 14w + 200

Collect like terms

16w - 14w = 200 - 150

2w = 50

w = 50/2

w > 25

Therefore, Steve's earning would be more than Carly's after 25 hours.

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The required experimental probability that the next batter will get a hit is 2/11.

A number that indicates how likely an event is to occur is called its probability. It is communicated as a number in the reach from 0 and 1, or, utilizing rate documentation, in the reach from 0% to 100 percent. The higher the probability, the more likely the event is to occur.

The experimental probability of an event happening is defined as the number of times the event occurs divided by the total number of trials or events.

In this case, we are given that 4 out of 22 batters have gotten a hit so far. Therefore, the experimental probability that the next batter will get a hit is:

P(hit) = Number of hits / Total number of batters

P(hit) = 4/22

Simplifying:

P(hit) = 2/11

Therefore, the experimental probability that the next batter will get a hit is 2/11.

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The mean amount of snow per day is equal to 19 cm snow per day.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

For the total amount of snow based on the frequency, we have;

Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)

Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135

Total amount of snow (s cm), F(x) = 570

Now, we can calculate the mean amount of snow as follows;

Mean = 570/30

Mean = 19 cm snow per day.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Given: 2r + 8 = 28 To solve for x, We need to get the variable on one side of the equation and the constant on the other. We can do this by adding or subtracting values to both sides of the equation.

2r + 8 - 8 = 28 - 8

=> 2r = 20

Now we can solve for r by dividing both sides by 2.2r/2 = 20/2

=> r = 10

Therefore, the answer is 10.The given equation is 2r + 8 = 28.

In order to solve for the variable, we need to isolate it on one side of the equation and the constant on the other side. To do that, we can subtract 8 from both sides:2r + 8 - 8 = 28 - 8

This simplifies to:2r = 20

Now we can isolate the variable r by dividing both sides by 2:r = 10

Thus, the solution is r = 10.

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The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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We need to check if 13 divides (20192018 - (1-1)") + 4H0. By performing the calculations, we find that 13 does not divide (20192018 - (1-1)") + 4H0. Hence, 20192018 is not divisible by 13.

To prove that 13 divides a number "a" if and only if 13 divides (an - (1-1)") + 4H0, we need to show that both conditions imply each other
First, let's assume that 13 divides "a". This means that "a" can be written as 13k, where k is an integer. We can express this in terms of base 10 as (13k - (1-1)") + 4H0. Simplifying further, we get (13k - 1) + 4H0. Since 13 divides 13k and 13 divides 4H0, it also divides their sum. Therefore, if 13 divides "a", it also divides (an - (1-1)") + 4H0.
Next, let's assume that 13 divides (an - (1-1)") + 4H0. This means that (an - (1-1)") + 4H0 can be written as 13k, where k is an integer. Simplifying the expression, we get an - (1-1)") + 4H0 = 13k. Rearranging, we have an = 13k + (1-1)") + 4H0. Since 13 divides 13k + (1-1)") + 4H0, it also divides their sum. Therefore, if 13 divides (an - (1-1)") + 4H0, it also divides "a".
In conclusion, we have proven that 13 divides "a" if and only if 13 divides (an - (1-1)") + 4H0.
To decide whether 20192018 is divisible by 13, we can apply the result from part (a). Let's express 20192018 as (an - (1-1)") + 4H0. Since 13 divides (an - (1-1)") + 4H0, if 13 divides 20192018, it will also divide (an - (1-1)") + 4H0. Therefore, we need to check if 13 divides (20192018 - (1-1)") + 4H0. By performing the calculations, we find that 13 does not divide (20192018 - (1-1)") + 4H0. Hence, 20192018 is not divisible by 13.

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By graphing both equations on the same axis and findin where do they intercept, we willsee that the solution is (-2, 6).

Here we have the following system of equations:

y = x + 8

y = -(1/2)x+5

And we want to solve it graphically.

To solve it in that way, we just need to graph both equations on the same coordinate axis and find the ponit where the graphs intercept, that point will be the solution for the system.

The graph of the system of equations can be seen in the image below:

There, we can see that the lines intercept at the point (-2, 6), so that is the solution of our system.

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